Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22627093 | C2 | semidirect |
| 4. C2×#64408⋊C16 | C2 | semidirect |
| 5. #22627011 | C2 | semidirect |
| 6. #22627006 | C2 | semidirect |
| 9. #17989709 | C4 | semidirect |
| 16. #17989688 | C4 | semidirect |
| 165. C73 | #12614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989709 | 2 |
| C2×#17989688 | 2 |
| #22627093 | 2 |
| C2×#64408⋊C16 | 2 |
| #22627011 | 2 |
| #22627006 | 2 |
| #22625708 | 2 |
| #12614 | 73 |